The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is $176$ cm$^3$, find the outer and

Question

The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is $176$ cm$^3$, find the outer and inner radii of the cylinder.

Accepted Answer

Step 1: Let outer radius be $r_2$ cm and inner radius be $r_1$ cm.
$	herefore r_2 - r_1 = 1$ ... (i)
Step 2: Volume of metal used $= 176$ cm$^3$
$\Rightarrow \frac{22}{7} 	imes 14 	imes (r_2^2 - r_1^2) = 176$
Step 3: $\Rightarrow r_2 + r_1 = 4$ ... (ii)
Step 4: Solving (i) and (ii), we get
$r_2 = \frac{5}{2}$ or $2.5$, $r_1 = \frac{3}{2}$ or $1.5$
Therefore, outer radius $= 2.5$ cm and inner radius $= 1.5$ cm

Question

Solution